Spin 1/2 in Modern QFT?

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1. May 17, 2015

referframe

The spin observable for spin 1/2 particles is represented by Pauli Matrices acting upon a 2-dimensional Hilbert Space. In RQM, forgetting about the matter-antimatter duality for the moment, that TWO-state Hilbert Space is directly related, through the Lorentz Group, to the TWO separate differential equations in the Dirac Equation. Is that same "TWO-ness" also found in modern QFT for spin 1/2 particles? Are there TWO separate quantum fields for a spin 1/2 particle in modern QFT? As always, thanks in advance.

2. May 17, 2015

atyy

The Dirac Equation holds in relativistic quantum field theory.

3. May 19, 2015

vanhees71

In addition one cannot stress early enough that a split of angular momentum in an orbital and a spin part is problematic in relativistic quantum field theory (to say the least). A thorough understanding of what's "spin" in relativistic QFT necessarily leads to Wigner's analysis of the irreducible unitary representations of the (quantum version of the) Poincare group. See

Weinberg, S.: The Quantum Theory of Fields, volume 1, Cambridge University Press, 1995

or my QFT lecture notes:

http://fias.uni-frankfurt.de/~hees/publ/lect.pdf

4. May 19, 2015